Frege-Geach-Hughes: Gapping Argument
I have an argument against some version of quasi-realism! Either David Velleman is wrong about Gibbard, or Gibbard is wrong about some of the facts.
David Velleman claims that Gibbard's response to the Frege-Geach problem requires that logical operators -- and I'd guess propositional operators ("believes that", "It is necessarily true that", etc.) -- be ambiguous. It goes like this: take, for example, "It is not the case that __". The standard account has it that negation expresses a function that takes a truth-value as an input and yields a truth value as an output. So, if the input is TRUE, then the output will be FALSE, and the other way around. But the Frege-Geach problem begins with noting that we can say things like the following "It is not the case that your pants are OK." If "It is not the case that __" expresses a truth-function, then this sentence ought to crash the semantic computation -- it ought to be semantically defective. It puts something that lacks a truth-value (on the Gibbardian view) into the scope of a truth-functional operator.
Gibbard's solution to the Frege-Geach problem is to generate a semantic value for moral statements that behaves like a truth-value -- it is bivalent and partitions a space of possible worlds. Gibbard's proposal aims to solve the F-G problem by providing proxies for truth-values -- i.e., truth-like-values.
Now, Velleman claims, operators like "It is not the case that ___" are going to be ambiguous on Gibbard's view. Sometimes they take truth-values as inputs and yield truth-values as outputs. Other times they take truth-like-values and yield truth-like-values.
In general, it is supposed to be a strike against a theory that it postulates ambiguity. I am not sure about that. But it clearly would be a mistake to postulate ambiguity where there is none. And I think there is reason to suppose that the postulated ambiguities don't exist.
Gapping Arguments, as they are called, can be used to test for linguistic ambiguity. If gapping is permitted in a context, then that is reason to suppose that there is no ambiguity in that context. If it is not permitted, then that is reason to suppose that there is ambiguity in that contenxt. You can gap across moral and non-moral contexts. You'll see what this stuff about gapping is all about by examining some examples.
Pardon the crude example, Grandma, but my imagination has been stunted by long exposure to undergraduates:
Claim: "Piss" (verb) is ambiguous.
Justification: "I pissed off John and into the snow." The test sentence is defective (ungrammatical) and so "pissed" is ambiguous. Gapping doesn't work here.
Consider by way of contrast "I ran into the store and then off to work." This test sentence does not show "ran" to be ambiguous. That is: it means the same thing when it takes "into the store" as an argument and when it takes "off to work" as an argument. Gapping does work here.
The Argument:
Claim: "It is false that ___" does gap when applied to moral statements and when applied to non-moral statements. So it ain't ambiguous in those contexts.
Justification: "It is false that those pants are wrong and, additionally, that 2+2 = 5." Gapping works here.
See also "I believe that 2+2 = 4; and that taking Rob's life is wrong, as well." Gapping works.
See also "I believe that 2+2 = 4 and Rob that Melissa is evil." Gapping works.
OK: so either Gibbard is wrong for having committed himself to the ambiguity claim, or he is not wrong because he isn't committed in the way Velleman claims. ...and I am a genius.
David Velleman claims that Gibbard's response to the Frege-Geach problem requires that logical operators -- and I'd guess propositional operators ("believes that", "It is necessarily true that", etc.) -- be ambiguous. It goes like this: take, for example, "It is not the case that __". The standard account has it that negation expresses a function that takes a truth-value as an input and yields a truth value as an output. So, if the input is TRUE, then the output will be FALSE, and the other way around. But the Frege-Geach problem begins with noting that we can say things like the following "It is not the case that your pants are OK." If "It is not the case that __" expresses a truth-function, then this sentence ought to crash the semantic computation -- it ought to be semantically defective. It puts something that lacks a truth-value (on the Gibbardian view) into the scope of a truth-functional operator.
Gibbard's solution to the Frege-Geach problem is to generate a semantic value for moral statements that behaves like a truth-value -- it is bivalent and partitions a space of possible worlds. Gibbard's proposal aims to solve the F-G problem by providing proxies for truth-values -- i.e., truth-like-values.
Now, Velleman claims, operators like "It is not the case that ___" are going to be ambiguous on Gibbard's view. Sometimes they take truth-values as inputs and yield truth-values as outputs. Other times they take truth-like-values and yield truth-like-values.
In general, it is supposed to be a strike against a theory that it postulates ambiguity. I am not sure about that. But it clearly would be a mistake to postulate ambiguity where there is none. And I think there is reason to suppose that the postulated ambiguities don't exist.
Gapping Arguments, as they are called, can be used to test for linguistic ambiguity. If gapping is permitted in a context, then that is reason to suppose that there is no ambiguity in that context. If it is not permitted, then that is reason to suppose that there is ambiguity in that contenxt. You can gap across moral and non-moral contexts. You'll see what this stuff about gapping is all about by examining some examples.
Pardon the crude example, Grandma, but my imagination has been stunted by long exposure to undergraduates:
Claim: "Piss" (verb) is ambiguous.
Justification: "I pissed off John and into the snow." The test sentence is defective (ungrammatical) and so "pissed" is ambiguous. Gapping doesn't work here.
Consider by way of contrast "I ran into the store and then off to work." This test sentence does not show "ran" to be ambiguous. That is: it means the same thing when it takes "into the store" as an argument and when it takes "off to work" as an argument. Gapping does work here.
The Argument:
Claim: "It is false that ___" does gap when applied to moral statements and when applied to non-moral statements. So it ain't ambiguous in those contexts.
Justification: "It is false that those pants are wrong and, additionally, that 2+2 = 5." Gapping works here.
See also "I believe that 2+2 = 4; and that taking Rob's life is wrong, as well." Gapping works.
See also "I believe that 2+2 = 4 and Rob that Melissa is evil." Gapping works.
OK: so either Gibbard is wrong for having committed himself to the ambiguity claim, or he is not wrong because he isn't committed in the way Velleman claims. ...and I am a genius.
posted by Idris at 3:45 PM
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